if det(A)=0 then the system ax=0 has free variables. explain the reason on the answer sheet


if det(A)=0 then the system ax=0 has free variables. explain the reason on the answer sheet...
Ax=O Unique solution (trivial solution x-0) No free variables Infinitely many (nontrivial) solutions Some free variables Every column of A is pivot column | (=> rank(A) = # of columns of A Some columns of A are not pivot columns rank(A)< #of columns of A You can use the above figure to answer the following questions are about homogeneous systems Ax-0. Answer TRUE or FALSE. If the answer is FALSE, choose FALSE with the appropriate counterexample, i.e example that shows...
Hi
Please answer the questions below. I do not need an explanation.
Just the correct answer. Thank you!
QUESTION 1 6 points Save Answer Consider a system Ax=b. Suppose the system has more equations than unknowns. Then it is possible for the system to have a unique solution. O O True False QUESTION 2 6 points Save Answer [-2 Given A=1 ( 9 3 1] -2 6 an 1 0 -1] , the (3,1)-entry of (A + B)' is [a]....
Vetermine whether each statement is true or false. If a statement is true, give a reason or ote an appropriate statement from the text. If a statement is false provide an example that shows that the statement is not true in all cases or cite an appropriate statement from the text. (a) The determinant of the sum of two matrices equals the sum of the determinants of the matrices. o, consider the following matrica ( 8 ) and (3) O...
Suppose a nonhomogeneous system Ax = b consisting of five linear equations with seven unknowns has a solution with three free variables. Is it possible to change some constants on the equations' right sides to make the new system inconsistent? Explain.
If A is a 2x3 matrix with two pivot positions, then Ax=0 has a nontrivial solution. True or false? please explain why, diagrams are helpful for me if possible
Question 2 One reason not to use global variables is that it makes a program hard to debug. True False
13. Determine whether the following assertion is true: let A be a 5x3 matrix. If Ax 0 has a single solution, then for every b the system Ax- b has a single solution 14. Determine whether the following assertion is true: let A be an n×n matrix, and x an nxl vector. The system AT-0 has a nontrivial solution if and only if the system Ax 0 has a nontrivial solution
13. Determine whether the following assertion is true: let...
I need to find det (lambda * x - A): The determinant for this
answer is: -x^3+7x-6. How can I get this answer?
8. (10 points) Find the general solution to the homogeneous system of DE: 3 2 6 x' = Ax where A = -2 -1 -2 -4) 1 -2
linear algebra question easy, please answer fast with steps
Mark each statement True or False. Justify each answer. Here A is an mxn matrix. Complete parts (a) through (e) below a. If B is a basis for a subspace H, then each vector in H can be wrben in only one way as a linear combination of the vectors in B. Choose the correct answer below O A. The statement is false. Bases for a subspace H may be linear...
Please answer True/False and explain why. Consider a modeling exercise that has 20 possible predictor variables. You apply both forward and backward variable selection based on AIC. Both variable selection methods will always return exactly the same model, i.e. both variable selection algorithms will select the same set of predictor variables.